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- W1522278055 abstract "A partial ordering $mathbb P$ is chain-Ramsey if, for every natural number $n$ and every coloring of the $n$-element chains from $mathbb P$ in finitely many colors, there is a monochromatic subordering $mathbb Q$ isomorphic to $mathbb P$. Chain-Ramsey partial orderings stratify naturally into levels. We show that a countably infinite partial ordering with finite levels is chain-Ramsey if and only if it is biembeddable with one of a canonical collection of examples constructed from certain edge-Ramsey families of finite bipartite graphs. A similar analysis applies to a large class of countably infinite partial orderings with infinite levels." @default.
- W1522278055 created "2016-06-24" @default.
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- W1522278055 date "2013-03-01" @default.
- W1522278055 modified "2023-09-27" @default.
- W1522278055 title "Ramsey Properties of Countably Infinite Partial Orderings" @default.
- W1522278055 doi "https://doi.org/10.37236/3151" @default.
- W1522278055 hasPublicationYear "2013" @default.
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